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Omni-MATH / A permutation of …(3,4,2,1,6,5,7) can be partitioned correctly into the blocks [3,4,2,1] and [6,5,7], since when these blocks are sorted, the permutation becomes (1,2,3,4,5,6,7). F…

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problem

A permutation of \{1,2, \ldots, 7\} is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation (3,4,2,1,6,5,7)(3,4,2,1,6,5,7) can be partitioned correctly into the blocks [3,4,2,1][3,4,2,1] and [6,5,7][6,5,7], since when these blocks are sorted, the permutation becomes (1,2,3,4,5,6,7)(1,2,3,4,5,6,7). Find the expected value of the maximum number of blocks into which the permutation can be partitioned correctly.
Plain-text mathematical notation (without MathML)
A permutation of \{1,2, \ldots, 7\} is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation (3,4,2,1,6,5,7) can be partitioned correctly into the blocks [3,4,2,1] and [6,5,7], since when these blocks are sorted, the permutation becomes (1,2,3,4,5,6,7). Find the expected value of the maximum number of blocks into which the permutation can be partitioned correctly.
Original LaTeX notation
A permutation of \{1,2, \ldots, 7\} is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation $(3,4,2,1,6,5,7)$ can be partitioned correctly into the blocks $[3,4,2,1]$ and $[6,5,7]$, since when these blocks are sorted, the permutation becomes $(1,2,3,4,5,6,7)$. Find the expected value of the maximum number of blocks into which the permutation can be partitioned correctly.

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task_id
d4cedc2b-0ed2-5391-9888-7d08999470a8
task_key
test--d4cedc2b-0ed2-5391-9888-7d08999470a8
task_revision_id
1
config / split
/ test

Official source

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